Quantum generative model for sampling many-body spectral functions

Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this paper we demonstrate how to utilize it compute dynamical response functions many-body systems. Specifically, design a circuit that acts as an efficient generative model, providing samples out spectral function high rank observables in polynomial time. This includes many experimentally relevant spectra such dynamic structure factor, optical conductivity, or NMR spectrum. Experimental realization algorithm, apart from logarithmic overhead, requires doubling number qubits compared simple analog simulator.